Abstract

Let $\Omega$ be a domain in $\mathbb R^n$ ($n\geq 2$). We find a
necessary and sufficient topological condition on $\Omega$ such
that, for any measure $\mu$ on $\mathbb R^n$, there is a function $u$
with specified boundary conditions that satisfies the Poisson
equation $\Delta u=\mu$ on $\Omega$ in the sense of distributions.